To assess the improved fit of mash compared with the simpler mash-bmalite, we used cross-validation; we fitted each model to a random subset of units (“training set”), and assessed fit by the log-likelihood on the remaining units (“test set”). We found that mash improved the test set log-likelihood very substantially (by 23,796; Supplementary Fig. 1). Further, mash placed 79% of the weight on the data-driven covariance matrices. These results confirm that our methods for estimating data-driven covariance matrices are sufficiently effective that they better capture most effects than do the canonical matrices used by existing methods.
